A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models
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A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models. / Durhuus, B.; Fröhlich, J.
In: Communications in Mathematical Physics, Vol. 75, No. 2, 06.1980, p. 103-151.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - A connection between ν-dimensional Yang-Mills theory and (ν-1)-dimensional, non-linear σ-models
AU - Durhuus, B.
AU - Fröhlich, J.
PY - 1980/6
Y1 - 1980/6
N2 - We study non-linear σ-models and Yang-Mills theory. Yang-Mills theory on the ν-dimensional lattice ℤv can be obtained as an integral of a product over all values of one coordinate of non-linear σ-models on ℤv-1 in random external gauge fields. This exhibits two possible mechanisms for confinement of static quarks one of which is that clustering of certain two-point functions of those σ-models implies confinement of static quarks in the corresponding Yang-Mills theory. Clustering is proven for all one-dimensional σ-models, for the U(n) ×U(n) σ-models, n=1, 2, 3, ..., in two dimensions, and for the SU(2) × SU(2) σ-models for a large range of couplings g2 ≳ O(ν). Arguments pertinent to the construction of the continuum limit are discussed. A representation of the expectation of Wilson loops in terms of expectations of random surfaces bounded by the loops is derived when the gauge group is SU(2), U(n) or O(n), n=1, 2, 3, ..., and connections to the theory of dual strings are sketched.
AB - We study non-linear σ-models and Yang-Mills theory. Yang-Mills theory on the ν-dimensional lattice ℤv can be obtained as an integral of a product over all values of one coordinate of non-linear σ-models on ℤv-1 in random external gauge fields. This exhibits two possible mechanisms for confinement of static quarks one of which is that clustering of certain two-point functions of those σ-models implies confinement of static quarks in the corresponding Yang-Mills theory. Clustering is proven for all one-dimensional σ-models, for the U(n) ×U(n) σ-models, n=1, 2, 3, ..., in two dimensions, and for the SU(2) × SU(2) σ-models for a large range of couplings g2 ≳ O(ν). Arguments pertinent to the construction of the continuum limit are discussed. A representation of the expectation of Wilson loops in terms of expectations of random surfaces bounded by the loops is derived when the gauge group is SU(2), U(n) or O(n), n=1, 2, 3, ..., and connections to the theory of dual strings are sketched.
UR - http://www.scopus.com/inward/record.url?scp=34250249553&partnerID=8YFLogxK
U2 - 10.1007/BF01222514
DO - 10.1007/BF01222514
M3 - Journal article
AN - SCOPUS:34250249553
VL - 75
SP - 103
EP - 151
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 2
ER -
ID: 330405157